We discuss theoretical background and experimental verification of advanced schemes for X-ray FELs using variable gap undulators (harmonic lasing self-seeded FEL, reverse taper etc.) Harmonic lasing in XFELs is an opportunity to extend operating range of existing and planned X-ray FEL user facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental. Another interesting application of harmonic lasing is Harmonic Lasing Self-Seeded (HLSS) FEL that allows to improve longitudinal coherence and spectral power of a SASE FEL. Recently this concept was successfully tested at the soft X-ray FEL user facility FLASH in the wavelength range between 4.5 nm and 15 nm. That was also the first experimental demonstration of harmonic lasing in a high-gain FEL and at a short wavelength (before it worked only in infrared FEL oscillators). Another innovative scheme that was tested at FLASH2 is the reverse tapering that can be used to produce circularly polarized radiation from a dedicated afterburner with strongly suppressed linearly polarized radiation from the main undulator. This scheme can also be used for an efficient background-free production of harmonics in an afterburner. Experiments on the frequency doubling that allowed to reach the shortest wavelength at FLASH as well as on post-saturation tapering to produce a record intencity in XUV regime are also discussed.